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Let $a',b',c'$ be the length of angle bisectors from angle $A,B,C$ in $\Delta ABC$ respectively. Find area of $\Delta ABC$ in terms of $a',b',c'$.

Diagram

My approach: $\Delta=1/2*a*a'*\sin(A/2+C)=1/2*b*b'*(B/2+C)=1/2*c*c'* \sin(C/2+A) a/ \sin A=b/ \sin B=c/ \sin C = abc/2\Delta$ then I don't know how to simplify. Or can it be simplified?

Mark
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Jack Koo
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  • Welcome to MSE. Please note that here you are expected to show your work, otherwise it may seem to readers that you are looking for volunteers to do your homework for free! Also, I suggest you can search among previously asked questions. You might find that your question (or something similar to it) has already been answered. Good luck! – Saeed Jul 01 '21 at 03:00
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    Saeed: Sorry I don't know the rules – Jack Koo Jul 01 '21 at 07:20
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    This is not my HW. This is just a random question appeared in my mind. – Jack Koo Jul 01 '21 at 07:21
  • I appreciate that you edited your post and added your approach. You can use the website's help for mathematical notation (https://math.stackexchange.com/help/notation). This way your posts will be easier to read. Also, to add photos to your post, consider uploading files rather than giving external links. – Saeed Jul 01 '21 at 15:57
  • sorry I do not have enough badge to add photo. – Jack Koo Jul 02 '21 at 14:51
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    Hi @JackKoo, I edited your question to use latex formatting (putting all the math in between dollar signs). That is the customary way to present math symbols on this website. – Mark Jul 02 '21 at 15:04
  • thank you very much – Jack Koo Jul 02 '21 at 15:08
  • How can he deduce d^2=bc/(b+c)^2*((b+c)^2-a^2)? – Jack Koo Jul 03 '21 at 01:05
  • Do he combine Stewart theorem and angle bisectors properties? – Jack Koo Jul 03 '21 at 01:07

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